This invention relates generally to improvements in controlling the growth process of a monocrystalline silicon ingot and, particularly, to a method and apparatus for accurately controlling the diameter of a monocrystalline silicon ingot during its growth process.
The Czochralski (CZ) process is used to obtain monocrystals. The most important application thereof is growing a monocrystalline silicon ingot, which is sliced into silicon wafers for fabrication of semiconductor circuits thereon. Briefly described, the CZ process includes melting a charge of polycrystalline silicon in a quartz crucible and lifting a monocrystalline seed from the surface of the melt silicon. As the seed is being lifted from the melted silicon, monocrystalline silicon grows from the seed and forms a cylindrical ingot. The modern CZ process produces silicon ingots having a diameter as large as 300 mm.
The key to produce silicon wafers with a uniform diameter is to produce silicon ingots with a uniform diameter along the length. It is well known by those skilled in the art that an increase in the pull-speed of the seed results in a reduction of the diameter of a growing silicon ingot therefrom and vise versa. It is also well known that an increase in the temperature of the silicon melt in the crucible results in a reduction of the diameter of a growing silicon ingot and vise versa. While diameter control sounds simple, it requires a sophisticated feedback control.
Conventionally, the CZ process is performed with the PID (proportional-integral-derivative) control method to control the diameter of a growing silicon ingot. The PID controller receives an error signal representing a difference between the target or desired diameter of a growing silicon ingot and the diameter of the silicon ingot actually observed. The PID controller then processes the deviation of the diameter as a function of time and transforms it into a pull-speed error. The pull-speed error is used to adjust the pull-speed of the seed.
Pull-speed control alone is usually insufficient to control the diameter of a growing silicon ingot satisfactorily. Thus, the CZ process is performed with additional PID controller specifically designed to control the temperature of the silicon melt in the crucible. The above pull-speed error is integrated over time to derive a temperature error. The derived temperature error, the target temperature from the temperature profile and the temperature actually measured are summed and provided to the second PID controller to adjust the temperature of the silicon melt.
Although the above described CZ process using two PID controllers to adjust both the pull-speed and the melt temperature simultaneously is widely used in producing silicon ingots, further improvements are needed to produce silicon ingots with diameters sufficiently satisfactorily uniform. In these days, the required standard for precisely and accurately controlling the intrinsic properties of silicon ingots during their growth has become much higher and stricter than it used to be. It is well known that variations of the pull speed that are performed to control the ingot diameter have a negative effect on a defect distribution within the ingot. It is further well known that pull speed variations have a negative effect on morphological stability during the growth of heavily doped ingots. It is therefore necessary to minimize the pull speed variations when controlling the diameter of the silicon ingot during the growth thereof.
Concerning the diameter and growth control, there are three categories of error sources that all lead to pull speed variations while growing silicon ingots to have them with a uniform diameter. The first category of error is caused by temperature fluctuations in the melt. It is well known that the temperature fluctuations in the melt are caused by buoyancy effects which bring about turbulences in the melt flow. Such temperature fluctuations cause changes of the crystallization rate, and such crystallization rate changes then cause changes of the ingot diameter. The diameter control system is designed to react to these diameter changes by outputting pull speed adjustments which result in pull-speed variations.
It is generally known that the melt flow turbulences can be reduced by applying a magnetic field which functions to reduce the melt temperature fluctuations and thereby reduce the pull speed adjustments by the diameter control system. The diameter deviations caused by the temperature fluctuations in the melt are more significant in small diameter ingots than in large diameter ingots, since the temperature fluctuations are localized in the melt, and the effects thereof are averaged over the cross section of an ingot if the diameter thereof is large. However, even under the condition that a large diameter ingot is grown within a magnetic field, there is still need for reducing the pull speed variations.
The second error source resides in the diameter feedback control itself and is caused by an inferior control model. Diameter control is customarily performed, using a PID controller. Those skilled in the art of control theory know that PID controllers are perfect for use in controlling systems that are governed by a linear differential equation of up to 2nd order. To some degree, PID control can also be used for controlling non-linear or higher order systems, but only in cases where the control performance and stability are not so important. When it is required to deal with systems that follow non-linear or higher order equations under the condition that the high control performance and high stability are needed, a specialized controller needs to be developed. However, because being convenient and also widely used, the conventional PID controllers are still used in the ingot diameter control, despite the fact that the required standard for control stability, or for reducing pull speed variations, is highly strict in these days and cannot be met by the conventional PID controllers.
The third source of error is caused by input errors, such as noise in an input signal of a diameter measurement indicative of the diameter of a growing ingot. Such noise in the input signal directly affects the diameter control system, causing unnecessary pull-speed variations. An error of this kind may not be so obvious in the prior art control systems because the prior art control systems usually suffer errors attributed to inferior control models adopted therein and such errors are large enough to dominate the input errors. However, an impact of the input errors on the control stability becomes obvious when a specialized control system is used in which an error from an adopted control model is small.